Non-commutative resolutions of quotient singularities
Abstract
In this paper we generalize standard results about non-commutative resolutions of quotient singularities for finite groups to arbitrary reductive groups. We show in particular that quotient singularities for reductive groups always have non-commutative resolutions in an appropriate sense. Moreover we exhibit a large class of such singularities which have (twisted) non-commutative crepant resolutions. We discuss a number of examples, both new and old, that can be treated using our methods. Notably we prove that twisted non-commutative crepant resolutions exist in previously unknown cases for determinantal varieties of symmetric and skew-symmetric matrices. In contrast to almost all prior results in this area our techniques are algebraic and do not depend on knowing a commutative resolution of the singularity.
Cite
@article{arxiv.1502.05240,
title = {Non-commutative resolutions of quotient singularities},
author = {Špela Špenko and Michel Van den Bergh},
journal= {arXiv preprint arXiv:1502.05240},
year = {2017}
}
Comments
Final version. Many corrections by the referee implemented